Is10645:2004 ('~f wm) Indian Standard METHODS FOR ESTIMATION OF PROCESS CAPABILITY AND PROCESS ( Second Revision) ICS 03.120.30 0 BIS 2004 BUREAU OF INDIAN STANDARDS MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG NEW DELHI 110002 August 2004 Price Group 6 Statistical Methods for Quality and Reliability Sectional Committee, MSD 3 FOREWORD This Indian Standard (Second Revision) was adopted by the Bureau of Indian Standards, after the draft finalized by the Statistical Methods for Quality and Reliability Sectional Committee, had been approved by the Management and Systems Division Council. Even when all the assignable causes of variation are removed from a process and it operates only under the chance causes, certain amount of variation is inevitable. This inherent variability of the process is generally referred to as process capability. Process capability is a statistical measure of inherent process variability and is defined as the length of natural process interval. It represents the variation that is obtained when the process operates under chance causes only. For example, on the processed parts, the process capability is the dimensional variation due to chance causes operating on a process or by known causes which cannot be eliminated or which are too uneconomical to eliminate. Process capability studies are useful for: a) Purchasing agent who has a means of comparing the actual performance of equipment with manufacturers' claims, b) Design engineer who has a more rational basis for the specification of tolerances when he is acquainted with the capability of the available equipment, c) Planning engineer in assigning the jobs to the $mriousmachines/processes after due consideration to the tolerances and ca~abilitie$, d) Production and ins~tion personnel in employing this as a basis for &weas control, and e) Organizations implementing IS/ISO 9000 standr@s on quality managementsystems. For assessing the capability of its processes, the methods described in this standard are intended to assist management of such organizations in this task. These indices need to be constantly reviewed by the management for keeping them at desired level and continuously improving them. Tool wear and other influences on a process such as temperature, pressme may cause a trend. For findkg the trend and its effect on process capability, reference maybe made to IS 397 (Part 3): 2003 `Method for statistical quality control during production : Part 3 Special control charts by variables'. The process capability includes/reflects the effects of factors contributing to the variability. The studies to optimize the levels of the factors and reduce the variability without adversely affecting the economy of production can be undertaken to improve process capability. Such studies do not form a part of this standard. It maybe noted that wherever the capability indices in this standard are computed, they only form point estimates of their true values. It is, therefore, recommended that wherever possible, confidence intervals for the indices are computed and reported. This standard was originally published in 1983 and revised in 1998. This revision has been undertaken to : a) Include the following: 1) factors influencing process variation, 2) planning the process capability study, and 3) action for process control on the basis of process capability and specification, b) Modify example for calculation of process capability using frequency method, c) Introduce the concept of process performance, and d) Incorporate many editorial corrections. The composition of the Committee responsible for the formulation of this standard is given in Annex B. IS 10645:2004 Indian Standard METHODS FOR ESTIMATION OF PROCESS CAPABILITY AND PROCESS PERFORMANCE ( Second Revision ) 1 SCOPE This standard defines process capability and covers the planning process capability study and its calculation for both variable (normal and non-normal distribution) and attributes type of data. This standard also describes the actions required to be taken when comparing process capability with specification limits. 2 REFERENCES The following standards contain provisions, which through reference in this text constitute provisions of this standard. At the time of publication, the editions indicated were valid. All standards are subject to revision and parties to agreements based on this standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below: IS No. 397 (Part 1): 2003 (Part 2): 2003 (Part 3): 2003 6200 (Part 3) :2003 Title Method for statistical quality control during production: Control charts for variables (second revision) Control charts for attributes and count of defects (third revision) Special control charts by variables Statistical tests of significance: Part 3 Tests for normality 3 TERMINOLOGY For the purpose of this standard, the definitions given in IS 7920 (Part 1) and IS 7920 (Part 2) shall apply. 4 FACTORSINFLUENCING PROCESS VARIATION Following are the major factors that influence the process variation: a) b) c) d) e) t) Condition of the machine or equipment, Skill of the operator, ~pe of operation and operational conditions, Raw materials used, Environment, and Measurement process. 5 PLANNING PROCESS CAPABILITY STUDY 5.1 The following points should be taken care of before taking up the process capability study : a) Study should be conducted by well trained and experienced personnel, b) Order of production should be preserved, c) Details of input materials, operational conditions, process lines and other facilities should be recorded, and d) The applicable specification limits, which may be either one-sided (lower or upper) or two-sided should be recorded. 5.2 A record of various stages of production should be kept during the study. The samples drawn for measurement should be identified as to stream, order of production, etc. The process should be operating under its normal operating conditions unless the study is investigating specific abnormalities. 6 PROCESS CAPABILITY 6.1 General 6.1.1 It is a statistical measure of inherent process variability and is defined as the length of natural process interval. It represents the variation that is obtained when the process operates under chance causes only. If the process was monitored using a control chart, it would be possible to detect the presence of any assignable cause(s) and eliminate them to ensure that the process operates of statistical 7200 (Part 1) :1989 Presentation data: Part 1 Tabulation and summarization (second revision) 7920 Statistical vocabulary and symbols: Probability and general statistical terms (second revision) (Part 2): 1994 Statistical quality control (second revision) (Part 1): 1994 9300 (Part 2) :1989 Statistical models for industrial applications: Part 2 Continuous models (/kit revision) 12348: 1988 Use of probability papers IS 10645:2004 under chance causes only. Any further reduction in the variability may need modification in the process or a technological upgradation in the process. 6.1.2 A process, which operates under chance causes only, that is in statistical control, can be described in terms of a probability distribution. The proportion of nonconforming items can be determined on the basis of this distribution. 6.1.3 The lower and upper natural process limits are obtained as a and (100 ­ a ) percentiles of the distribution and these include (100 - 2a) percent of the items when the process is in a state of statistical control. They are written as Pa and Pcl{M_aJ [where 100 P (X< P=)= a]. The value of a can generally be chosen on considerations of coverage and length of the interval. For a normally distributed process, the natural process limits are taken as p A3a and they correspond to a = 0.135. Even for nonnormal distributions, the percentile values may be taken corresponding to et = 0.135 therefore Pu = P0,,35. In such a case, the natural process limits will not necessarily be symmetrical around the process mean. The natural process interval (also called the process spread), namely, the interval between the upper and the lower natural process limits, covers 99.73 percent of items produced (see Fig. 1 and Fig. 2). 6.1.4 In short, it will be necessary to: a) Define the process and its operating conditions. If there is a change in those conditions it will necessitate a fresh process study, b) Make the process stable and bring it into statisti. cal control, c) Estimate the inherent process variability, and d) Select an appropriate measure of process capability. 6.1.5 It is necessary to check from the control chart if the process is in statistical control [see IS 397 (Part 1) or IS 397 (Part 2)] and/or from a histogram of the data [see lS----'lzuu (~art""'" 1)J. An ` appropriate " test ror - normallty "" [see " IS 6200 (Part 3)] or normal probability paper (see IS 12348) may also be used to look for the following: Departure from normality, Outliers, Data beyond specification limit, Location of the specification limits in relation to the distribution, e) Asymmetry (that is skewness), t) `Long tails' in the data (that is kurtosis), and g) Any other unusual features. 6.1.6 It would be inappropriate to just discard data that do not appear to fit any pre-conceived pattern. Such departures might be very revealing about the behaviour of the process and should be thoroughly investigated. 6.1.7 In case of multi-output processes (such as multispindle machines, multi-nozzle filling machines), process capability has to account for extra sources of variation that may be present from one output point to the other. The distribution of observed values on items coming from different output points may still be normal but with larger variability. It is important to state how the standard deviation has been cakulated as well as the sampling strategy used, sample size and the quantity produced for each output point (see 7.1). 6.2 Data are usually taken from a control chart. If the control chart has relaxed or modified control limits, the standard deviation will be larger than that estimated from data taken from a control chart with standard control limits. Issues such as these and those given earlier will influence the determination of natural process interval and it is important that they are stated in any capabili~y' assessment. 6.3 Variable Data -.. ~. , 1] 135 >; a) b) c) d) FIG. 1NATURAL PROCESS INTERVAL-NORMAL DISTRIBUTION P 0,,3 1'w.!65 /\ , 0135Z , ,.J -... <.. -. `\. \ \.. !33 73 %------ 6.3.1 Normal Distribution When the quality characteristic follows a normal distribution, process capability is defined as 6a where o 2 DmUnON FIG. 2 NATURAL PROCE+S INIERVAL-NON- NORMAL 1s 1U645 : mJu4 is the standard deviation of test results from the process under statistical control. This is equal to the length of the natural process interval as shown in Fig. 1. NOTE -- The process mean v and the process standard deviation c can be estimated in terms of sample mean z and sample standard deviation s. Process Capability may be estimated by 6 s. 6.4.2 Process CapabiliQ as Number of Non-conformities per Item When a process is monitored using a c-chart [see IS 397 (Part 2)], the process capability maybe described as the average number of non-conformities, ~, once the process is in statistical control (see 11.4). NOTE -- The process capability is calculated by using the estimate average of proportion of non-conformities as obtained from the data using control charts. It is first ensured that the control chart shows that the process is in statistical control [see IS 397 (Part 2)]. 7 6.3.2 Other Distributions 6.3.2.1 When the quality characteristic does not follow a normal distribution, the natural process limits PO,lq~ and P~9,M5 are determined either by use of tables giving the area under the probab~lity distribution curves [see IS 9300 (Part 2)] or using the probability papers [see 1S12348] or by integration or by use of numerical methods for evaluation of integrals. The length of the natural process interval PW,865 ­ P0,135 (when the process is in the state of statistical control) is defined as process capability [see Fig. 2]. 6.3.2.2 For the non-normal distribution, like exponential or weibull or log-normal the percentiles Pa, P(lm.a) may be expressed as functions of the population mean and the population standard deviation. The mean and standard deviation may be estimated by the sample average z and sample standard deviation s. Hence, estimates of these percentiles may be obtained in terms of the sample mean and sample standard deviation. P~l{m. ~,­ Pa is the process capability. 6.3.2.3 The mean and standard deviation and hence the percentiles may also be estimated using control charts and probability papers. 6,4 Attributes Data It is often the case with attribute quality characteristics that the objective is zero non-conformities or zero nonconforming items. Consequently, process capability is defined in terms of the process average of number of nonconformities or proportion of non-conforming items, for example, ~ or >, when the process is in the state of statistical control. 6.4.1 Process Capability conforming Items as Proportion of Non- PROCEDURES FOR ESTIMATING PROCESS CAPABIL~ FORVARL4BLE DATA 7.1 Using Range Method 7.1.1 For single output machine, 25 sub-groups of 3 to 5 continuous observations are recommended. 7.1.2 For multi-output machines (such as multiple spindle machines or multiple filling heads) or transfer lines wherein identical parts are processed either on many outputs or on a chain of machines, samples shall be taken output-wise or receiving station-wise. This is necessary to identify the output or the station which turns out nonconforming parts. In these cases, 5 samples of 3 to 5 observations each are taken from each output or line subject to a minimum of 30 samples. 7.1.3 It is advisable to keep the samples taken in separate trays according to the machine, time of taking sample, output, etc. The evaluation of measurement values is done by the range method. 7.1.4 Record the measured values in the prescribed form in the order of manufacture. 7.1.5 Calculate the range for each sub-group, difference between the largest and smallest value. the 7.1.6 The ranges are then homogenized as described in 6.2.2.1 of IS 397 (Part 1). 7.1.7 The estimate of standard deviation (s) is given by ~ Idz where ~ is the average of the homogenized ranges and dz is a constant factor obtained from Annex A for a given value of sample size (n). 7.1.8 The value of 6 ~ /d2 is calculated, which is the process capability. 7.1.9 If the ranges are not homogenized, even after the elimination of 25 percent of the sub-groups, the data is discarded and fresh data is collected after removing the assignable causes of variation and above procedure is repeated. When a process is monitored using a P-chart [see IS 397 (Part 2)], the process capability maybe described as the average proportion of non-conforming items, when the process is in statistical control (see 11.3). NOTE -- The process capability is calculated by using the estimate of average proportion of non-conforming items as obtained from the data using control charts. It is firsi ensured that the control chart shows that the process is in statistical control [see IS 397 (Part 2)]. 3 IS 10645:2004 7.2 Using Frequency Distribution Method 7.2.1 For single output machine, as far as possible, a sample of minimum 50 consecutive pieces is taken after confirming that the process is in statistical control. 7.2.2 From the data, the frequency table is obtained [see 5 of IS 7200 (Part l)]. 7.2.3 The data is then tested for normality [see IS 6200 (Part 3)]. If the data follow normal distribution, calculate standard deviation (s). 7.2.4 The value of process capability is then obtained as six times the standard deviation that is 6 s. NOTE -- The sample sizes recommended are for engineering industry and may vary with industry and situations. of the specifiedtoleranceto the naturalprocess interval when the process is under statisticalcontrol and is defined w cP=p U­L .pa 100-a where U and L are the upper and lower specification limits and Plm.., f. are percentiles of the distribution. NOTES 1 Generally the vahse of a is taken as 0.135. 2 Process capability fraction -- The inverse of the CP index (denoted by CR) is called process capability fraction. N may be expressed as percentage. 9.1.1 The upper process capability index (CP~u), in relation to upper specification limit is defined as: C* = 8 PROCESS CAPABILITY AND SPECIFICATION LIMITS 8.1 Capable processes are those whose natural process intervals are less than the specified tolerance (see Fig. 1 and Fig. 2). In other words, the process capability, that is 6rJ or Pw,8h5­ P0,1J5 is less than the (U­ L), where U and L are the upper and the lower specification limits respectively. Under these circumstances there is some latitude for shift in process average. It is advisable not to consume this latitude, particularly where these are likely to affect subsequent assembly operations, if any. 8.2 Even if a process is deemed capable by the above definition, if the process distribution has been poorly centered relative to the specification limits, out-oT-specificationitems may be produced. For this reason, it is necessary to assess the location in addition to the length of natural process interval. This consideration leads to defining process capability indices (see 9). 8.3 The information that is derived from process capability can be effectively used in the process control. The foremost of them is to compare process capability with the tolerance. 8.4 Depending upon the relationship between the process capability and the difference between the upper specification Iimit (U) and the lower specification limit (L), Table 1 suggests probable actions to be taken. 8.5 In the case of one sided limit, that is, when either upper specification limit (U) or lower specification limit (L) is given, the probable actions to be taken are suggested in Table 2. 9 PROCESS CAPABILITYINDICESFORVARIABLE DATA 9.1 The process capability index is defined as the ratio (u - PJ/(Pw,w5 - Pm) 9.1.2 The Iowerproeess capability index (C&l),in relation to lower specification limit is defined as: c Pkl = (Pm- L)/( Pm - PO,lJ 9.1.3 The minimum process capability index (CPJ, is defined as: Cpk = Minimum{ C*U,C,N) NOTE -- Cpk= Cp (1- k) where k is a factor s 1 and for PM= (U+L)/2, CPk = CP. Bench mark of CX= 1.33 is often used but C*=2 is needed to ensure that moderate changes in the process do not result in parts beyond specification limits. 9.1.4 In case when only U is given, the value of C kuis to be taken as CPk and if only L is given, the value o~CP~l is to be taken as Cpk. 9.1.5 These indices will provide information whether a process is poorly located and whether it will produce out-of-specification items. Even if the process capability index (CJ is high, a low value of the performance index (CPJ will reveal a poorly located process producing outof-specification items. 9.2 For normal distribution, the natural process interval is P,m_~­ Pa= 6G, therefore the process capability index is defined as: Cp = (U- L)16G 9.3 A value of 1.67 for CP is highly desirable. Further, for normal distribution: c ,ku = (u- p)/3c CPM= Qt- L)/ 3C Cpk = Minimum {Cpku> c,,,) 4 IS 10645:2004 Table 1 Process Capability and Specified Tolerance ('Ikvo-SidedSpecification) (Clause 8.4) S1 No. (1) i) Relationship (2) Process capability c (U-L) 1) 2) 3) ProbableActions/Decisions (3) Job cars be changed to a less costly/precise machine. Specified tolerance cars be narrowed if it is economical y worthwhile. Inspection intervrd can be increased and 100 percent inspection if employed cars be d&tc.nsed with. The items can be accepted on the basis of control chart as long as it shows that the process is in control. Process average can be set at an economical level closer to the uPWr (~ or lower(~) specification limit depending on the situation. If it is advamagcmss to be nearer L set at L + 36 and in the latter case set the process average at U -30. If economical setting is immaterial, maintain ~ chart with related modified con-&l limits for optimal re-s;t~ings. When s is known: UCL = U - V,o LCL = L + V,u Wbcn cr is not known: UCL=U-V2~ LCL=L+V2~ where the values of V, and V2may be obtained fmm Annex A. 5) Centering of process at (U+L)/2 is essential for mating components Greater attention to the centering of the process (maintaining the process average at the specification mean) should be given. Set the machine at the most economic level if it is advantageous to change the proxss average at the risk of allowing some scrap or rework. 3) Investigate the possibility of reducing process variability. Scrap and rework are inevitable. Resort to minimum machine adjustments. Hundred percent inspection must be resorted to. Examine the possibility of widening the specified tolerance to suit the processcapability. ExplorE changes in the process reduce its variability. Switch over to more precise/costly machines. Maintain ~ - R charts and set the machine at (U+L)/2 (for minimum total rejections) followed by 100 percent inspection. Maintain ~ - R charts and set the machine at the most economic level. Calculation of the most economic level is as follows : Let `A'be tbe loss, if ~ `B' be the profit, if Ls y (UZ.) 1) 2) 3) 4) iv) Long-term solutions 1) 2) v) Short-term/immediate solutions 1) 2) `C' be the loss, if ~ > U The most economic level for machine setting is: U+L+ --2 a2 @"'"-"GziG 5 IS 10645:2004 Table 2 Process Capability and One-Sided Specification (Upper Limit) (Clause 8.5) S1 No. Relationship (2) Process capability < 2 (U - Processaverage) a) Probable ActionsAecisions (3) There is adequate safety margin. Non-conforming items do not occur If production can be increased or it is otherwise advantageous, set the machine at the level U -3 rr and maintain control chart for both average and range Explore possibility of gains through reduction corresponding appropriate raise in the average in c and (1) i) b) c) ii) Process capability = 2 (U - Process average) Process capability > 2 (U ­ Process average) NOTE -- When lower specification Maintain control chart for both average and range to ensure conformance Investigate the possibility of reducing the machine setting arsd/or machine variability compatible with the rcquirwments. iii) limit(~) k specified, (~ - Process average) should be replaced by (Process average - L.) and (.J-31s by L.+30in the table. 10 PROCESS PERFORMANCE VARIABLE DATA INDICES FOR Therefore, the PPkindices can be expressed as: PPku P Pkl = (u-p)/3cJ or L)/ 30 10.1 Process performance, a statistical measure of the outcome of a characteristic from a process which may not have been demonstrated to be in a state of statistical control, is effectively expressed by indices covering situations where specification limit(s) are given. These indices are based on both the location and the spread of the distribution. 10.2 The process performance index is the ratio of the difference between a specified tolerance limit and the process location to the difference between the corresponding natural process limit and the process location. It is known as the F'P~ index which is defined in terms of upper process performance index and lower process performance index as the lower of the two. Thus P= Pku P= Pkl P,k where U and L are the upper and lower specification limits respectively, and Pgq,8f5, P*O and P0,,~5 are the percentile values of the distribution. 10.3 When the variable follows a normal distribution, the median P~Ois equal to the mean (w). Further, (P(),,,65 - P50) and (P50­ PO,J are each equal to 3 cr. (U - PJ/(PW,,b, - P,,) (also called upper process performance index) (P50- L)/(P50- PO,lJ (also called lower process performance index) and = minimum (PP,U, PPJ = (p- where U and L are upper and lower specification limits and `c' the inherent process standard deviation. Ppk = Minimum {Ppku, `Pkl) 11 ILLUSTRATIVE EXAMPLES 11.1 Table 3 gives frequency and Table 4 gives the values of diameter of 150 observations for breakhg load (in kN) of aluminium wires (size 300 mm) drawn according to IS 398( Part 3) when the process is in statistical control. The mean and standard deviation of the above data have ken calculatedas(~) 1.39and (s) 0.11 respectively.Using %2 - test for testing goodness of fit [see IS 6200 (Part 3)], it has been found that the data follow normal distribution. Hence, process capability = 6s = 6 x O.11= 0.66 11.2 Estimation of Process Capability Using Range Chart Component Characteristic Specification : Bearing bush : Internal diameter in mm, of bearing bush : 28.020~"021mm Deviates from Table 5 gives recorded observation: 28 mm in units of thousands. 6 IS 10645:2004 11.2.1 Computations R-Chart i = 145/25= 5.8 CL UCL =D, ii = 2.282x5.8= 13.24 Since the range for sub-group number 21 is more than UCL, this sub-group is eliminated for the purpose of homogenization. For the remaining 24 sub-groups, average range ( ~ ) and UCL are calculated as follows: i = (145 - 15)/24 = 130/24 = 5,42 = F = 74~,6­29.2­ 25.8 = ==29.94 23 23 . homogenized follows: X, for the above data is obtained as UCL = ? + Az ~ = 29.94 + 0.729X 5.09 = 33.7 LCL = ~­Az~= = 26.2 29.94 + 0.729X 5.09 UCL = D,% = 2.282X 5.42= 12.37 Again, since the range for sub-group number 11 is more than UCL, it is eliminated for the purpose of homogenization. For the remaining 23 sub-groups: I = (130- 13)/23 = 117/23 =5.09 = 2.282X 5.09 = 11.62 As average for sub-group number 2 is more than UCL and that for sub-group number 9 is less than LCL, these are eliminated for the purpose of homogenization. For the remaining 21 sub-groups: CL = 29.87 = ~ = 688,6 ­ 36.5 ­24.s = ~ 21 21 UCL = D,~ UCL = X+ A2~ = 29.87 + 0.729X 5.09 = 33.6 LCL = X- A2~ = 29.87 + 0.729X 5.09 Now, as all the ranges are below UCL, the process is in statistical control. Process Capability = 6 CJ = 6 ~ /d2 =6x 5.09/2.059= 14.8 where value of d2 for n = 4 is obtained from Annex A. However, for calculation of CP~ (see 9.1.4), the value of . homogenized X, may also be required. In such cases, = 26.2 Now, as all the average values are within UCL and LCL, these are taken as control limits for average chart for future purposes. Table 3 Frequency Table (Clause 11.1) S1 No. (1) i) ii) Class Interval (2) 1.125-1.175 1.175 ­ 1.225 1.225 ­ 1.275 1.2751.3251.3751.4251.4751.325 1.375 1.425 1.475 1.525 Tally Marks (3) 1111 W Ill U+fi+f+ll #it w ## 1111 If#w+fiituft llll #fttf#uft#it Frequency (4) 4 8 12 19 24 29 19 14 12 7 2 Total 150 iii) iv) v) vi) #+tllll vii) M+1111 M ?w+ +/if/if+1111 iitft++lll /%/II II viii) ix) 1.525 ­ 1.575 1,575 ­ 1.625 1,625 ­ 1.675 x) xi) 7 IS 10645:2004 Table 4 Breaking Load (in kN) of Aluminium Wires (Size 300 mm) (Clause 11.1) 1.30 1.49 1.45 1.35 1.42 1.43 1.41 1.45 1.50 1.40 1,41 1,28 1.37 1.44 1.46 1,39 1.28 1.48 1.38 1.41 1.47 1.40 1.38 1.33 1.31 1.38 1.42 1.34 1.33 1.35 1.46 1.40 1.53 1.48 1.25 1.34 1.58 1.36 1.19 1.45 1.26 1.21 1.32 1.63 1.40 1.41 1.35 1.34 1.30 1.28 1.46 1.40 1.58 1.53 1.36 1.27 1.42 1.37 1.34 1.44 1.51 1.52 1.24 1.39 1.19 1.20 1.35 1,36 1.24 1.31 1.39 1.31 1.21 1.36 1.26 1.38 1.57 1.35 1.50 1.30 1.61 1.59 1.53 1.60 1.36 1.20 1.33 1.44 1.31 1.42 1.27 1.23 1.13 1.17 1.31 1.48 1.37 1.48 1.43 1.31 1.42 1.37 1.41 1.27 1.37 1.52 1.55 1.62 1.50 1.34 1.27 1.45 1.53 1.56 1.57 1.32 1.40 1.49 1.14 1.37 1.41 1.39 1.55 1.32 1.46 1.65 1.50 1.39 1.27 1.33 1.51 1.60 1.43 1.20 1.46 1.22 1.17 1.28 1.43 1.47 1.40 1.42 1.38 1.45 1.30 1.50 1.56 1.31 1.30 1.27 c P = (U- L)/6~ld2 = (? = 1.42 *l.34 1.50 less than UCL, it is inferred that the process is under statistical control. The process capability is given by the estimate of average proportion of non-conforming items that is, > =0.04. 11.4 Process Capability Using c-Chart Table 7 gives the axle HSG reworkdata. Total non-conformities =90 z = 90/30=3 c pkl c pk. -L)J3~ld, ~)13~ld,= = (u. CP~,)= 1.34 Cpk = Minimum (CPku, Since CP and CP~are greater than 1.33 the process is capable, however, the performance is not satisfactory since the process shows occasional out of control points. 11.3 Process Capability using p-Chart Table 6 gives the weld shop petrol inspection data. Total non-conforming items =48 1' = 48/(30X 40)= 0.04 &~; = ~30x 0.04 X 0.96= G n~ +3x1.07 = 1.07 UCL = E +34?= 3+343 = 3+5.2 =8.2 As the values of number of non-conformities for all subgroup are less than UCL, the process is in statistical control. The process capability is given by the estimate of average number of non-conformities per unit that is, z =3.0 UCL= CL =1.2+ 3.2=4.4 = O LCL=O As all values of number of non-conforming items are 8 IS 10645:2004 Table 5 Data on Internal Diameter, in mm, of Bearing Bush (Clause 11.2) Sub-group No. (1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 / I (2) 29 37 28 26 31 34 30 26 22 24 24 32 28 32 34 32 36 35 29 31 23 28 27 28 32 (ID-28)X 1000 A 11 111 (3) 30 36 26 35 34 30 34 27 27 28 37 36 30 25 32 33 26 29 29 33 20 26 29 33 34 (4) 24 36 28 29 29 34 27 30 26 32 26 33 31 27 28 31 27 28 28 30 35 32 27 28 28 Average Iv (5) 29 37 28 27 29 29 28 28 24 32 30 30 31 30 34 31 33 32 28 29 25 26 28 32 32 Range (R) (7) 6 1 2 9 5 5 7 4 5 8 I 32) 6 3 7 6 2 10 7 I 4 151J 6 2 5 6 (y) (6) 28.0 36.5' 27.5 29.2 30.8 31.8 29.8 27.8 24.811 29.0 29.2 32.8 30.0 28.5 32.0 31.8 30.5 31.0 28.5 30.8 25.8 28.0 27.8 30.2 31.5 Total i)Eliminatedin first homogenization. ~)Eliminatedin second homogenization. Table 6 Weld Shop Patrol Inspection Data Sub-group Size =30 (Clause 11.3) Sub-group No. (1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Non-conforming (2) 2 1 3 2 1 2 1 1 2 0 0 1 1 2 1 2 1 0 3 0 Items Sub-group No. (1) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 743.6 145 Non-conforming (2) 0 2 0 3 0 0 2 0 I 0 2 1 1 0 2 3 2 1 0 2 Items 9 IS 10645:2004 Table 7 Axle HSG Rework Data Sub-group Size = Each Axle (Clause 11.4) Sub-group No. (1) 1 Number of Nou-conformities (2) 4 3 2 1 2 2 1 4 5 3 3 8 4 5 3 sub-group No. (1) 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Number of Non-conformities ('2) 3 2 1 2 2 2 4 I 4 3 1 2 5 2 6 2 3 4 5 6 7 8 9 10 11 12 13 14 15 10 IS 10645:2004 ANNEX A ( Clause 7.1.7 and Table 1) FACTORS FOR COMPUTING CONTROL LIMITS AND MODIFIED CONTROL LIMITS No. of Observations in the Sample n (1) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 d, A, DB D, v, Using Known Standard Deviation (6) 0.879 1.268 1.500 1.658 1.775 1.866 1.939 2.000 2.051 2.095 2.134 1.168 2.198 2.225 v, Using Average Range R (7) 0.779 0.749 0.729 0.713 0.700 0.690 0.681 0.673 0.666 0.660 0.655 0.650 0.645 0.641 (2) 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.173 3.258 3.336 3.407 3.472 (3) 1.880 1.023 0.729 0.577 0.483 (4) 0 0 0 0 0 (5) 3.267 2.575 2.282 2.115 2.004 16 17 18 19 20 3.532 3.588 3.640 3.689 3.735 2.250 2.272 2.293 2.312 2.329 0.637 0.633 0.630 0.627 0.624 21 22 23 24 25 3.778 3.819 3.858 3.895 3.931 2.345 2.360 0.374 2.388 2.400 0.621 0.618 0.615 0.613 0.611 for large sample sizes, the entries in CO1 3, 4 and 5 have not been given beyond n =6. NOTE-- Sincerangeis not recommended ANNEX B (Foreword) COMMI'ITEECOMPOSITION Statistical Methods for Quality and Reliability Sectional Committee, MSD 3 Organization Kolkata University, Koikata Bharat Heavy Electrical Limited, Hyderabad Representative PROF S. P. MUKHSRJEe(CJurfrrmm) SHRIS. N. JHA SHRIA. V. KRSSHNAN (Alternate) Continental Devices India Limited, New Delhi DR NAVSN KAPUR SIituVUWL GUPTA(Alternate) 11 IS 10645:2004 Organization Directorate General of Quality Representative(s) SHst S. K. SRIVASTVA LT COL P. VUAYAN (Alternate) Assurance, NewDelhl Laser Science and Technology Centre, DRDO, New Delhi Escorts Limited, Faridabad HMT Ltd. R&D Centre, Brmgalore Indian Agricultural Statistics DRASHOK KUMAR SHKJC. S. V. NARENDRA SHRIK. VOAYAMMA DR S. Research Institute,NewDelhi D. SHARMA DRA. K. SRSVASTAVA (Alternate) Indian Association for Productivity, Quality & Reliability, Kolkata Indian Institute of Management, Lucknow Indian Statistical Institute, Kolkata DRB. DAR s. CHAKRASORTY PRGF PROFS. R. MOHAN PRCW ARVIND SETH (Alternate) National Institution for Quafity and Reliability, New Delhi SHRtY. K. BHAT SHRIG. W. DATEY (Alternate) Powergrid Corporation of India Limited, New Delhi DR S. K. AGARWAL SHRID. CHAKRABORTY (Allernae) SRF Limited, Chennai SHRIA. SANJEEVA RAG SHRJ C. DEStGAN (Alternate) SHRIS. K. KIMOTHI SHJUP. N. SIGKANTH (Alternate) Standardization, Testing and Quality Certification , New Delhi TELCO, .lamshedpur SHIUS. KUMAR SHW SHANTI SARUP(Alternate) University of Delhi, Delhi - In personal capacity (20/1, Krishna Nugac Safdurjung Enclave, New Delhi i 10029) In personal capacity (B-109, Mulviyu Naguc New De[hi 110017) BIS Directorate General M.C. Ptzov AGRAWAL SHIUD. R. SEN PROI=A.N. NANKANA SHW P. K. GAMBHIR,Dkector & Head (MSD) [Representing Director General (Ex-oficio)] Member Secretuty SHRILALITKUMAR MEHTA Joint Director (MSD), BIS Panel for Process Control, MSD 3/P-2 In personal capacity (B-109, Mulviyu Naguc New Delhi 11W17) P~oF A. N. NANKANA (Convener) SHRIY. K. BHAT DR S. National Institution for Quality and Reliability, New Delhi Powergrid Corporation of India Limited, New Delhi Standardization, Testing and Quality certification, New Delhi TELCO, Pune In pcrwnal capacity (20/1, Krishna Nugan Sqfdarjrstr~tkluve, New Delhi 110029) K.AGARWAL SHRI S. K. KIMIYtHI SARUP SmztSHANTI SHIUD. R. SEN 12 Bureau of Indian Standards BIS is a statutory institution established under the Bureau of Indian Standards Act, 1986 to promote harmonious development of the activities of standardization, marking and quality certification of goods and attending to connected matters in the country. Copyright BIS has the copyright of all its publications. No part of these publications may be reproduced in any fom~ without the prior permission in writing of BIS. This does not preclude the free use, in the course of implementing the standard, of necessary details, such as symbols and sizes, type or grade designations. Enquiries relating to copyright be addressed to the Director (Publications), BIS. Review of Indian Standards Amendments are issued to standards as the need arises on the basis of comments. Standards are also reviewed periodically; a standard along with amendments is reaffkmed when such review indicates that no changes are needed; if the review indicates that changes are needed, it is taken up for revision. Users of Indian Standards should ascertain that they are in possession of the latest amendments or edition by referring to the latest issue of `BIS Catalogue' and `Standards: Monthly Additions'. This Indian Standard has been developed from Doc: No. MSD 3 (238). 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